A particle moves along a straight line such that its acceleration is a = (42 - 2) m/s? where t is in seconds. When t = 0, the particle is located 2m to the left of the origin, and t = 2s, it is 20m to the left of the origin. Determine the position of the particle when t = 4

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. A particle moves along a straight line such that its acceleration is a = (42 - 2) m/s?
where t is in seconds. When t = 0, the particle is located 2m to the left of the origin,
and t = 2s, it is 20m to the left of the origin. Determine the position of the particle
when t = 4 s.


2. A particle is moving along a straight line with the acceleration a =12t - 3t2 ft/52,
where t is in seconds. Determine the velocity and the position of the particle as a
function of time. When t = 0, v = 0 and s = 15 ft.


3. A ball is released from the bottom of an elevator which is travelling upward with a
velocity of 6 m/s. The ball strikes the bottom of the elevator shaft in elevator shaft in
3s. Determine the height of the elevator from the bottom of the shaft to the instant
the ball is released, and find the velocity of the ball when it strike the bottom of the
shaft.


4. A particle moving along a straight line is subjected to a deceleration a =
-20m/52
where v is in m/s. If it has a velocity v = 8 m/s s = 10 m when t = 0, determine its
velocity.


5. The position of the particle is given by s=(2t^2- 8t + 6) m, where t is in seconds.
Determine the time when the velocity of the particle is zero, and the total distance travelled
by the particle when t = 3 s.


6. A particle travels along a straight line with an acceleration of a = (10 - 0.2s) m/s3, where s is
measured in meters. Determine the velocity of the particle when s = 10 m if v = 5 m/s at s = 0.

7.Two particles A and B start from rest at the origin s = 0 and move along a straight line such
that a = (6t - 3) ft/s? and ag = (12t2 - 8) ft/s?, where t is in seconds. Determine the distance
between them when t = 4 s and the total distance each has travelled in t = 4 s.

8.When a particle is projected vertically upwards with an initial velocity of Vo, it experiences anacceleration a=                 -(g+kv?), where g is the acceleration due to gravity, k is a constant and v is
the velocity of the particle. Determine the maximum height reached by the particle.

1. A particle moves along a straight line such that its acceleration is a = (4t² - 2)m/s²,
where t is in seconds. When t = 0, the particle is located 2m to the left of the origin,
and t = 2 s, it is 20m to the left of the origin. Determine the position of the particle
when t = 4 s.
3tz ft/s²,
2. A particle is moving along a straight line with the acceleration a = 12t
where t is in seconds. Determine the velocity and the position of the particle as a
function of time. When t = 0, v = 0 and s = 15 ft.
3. A ball is released from the bottom of an elevator which is travelling upward with a
velocity of 6 m/s. The ball strikes the bottom of the elevator shaft in elevator shaft in
3s. Determine the height of the elevator from the bottom of the shaft to the instant
the ball is released, and find the velocity of the ball when it strike the bottom of the
shaft.
4. A particle moving along a straight line is subjected to a deceleration a = -2v m/s²,
where v is in m/s. If it has a velocity v = 8 m/s s = 10 m when t = 0, determine its
velocity.
5. The position of the particle is given by s = (2t2 8t + 6) m, where t is in seconds.
Determine the time when the velocity of the particle is zero, and the total distance travelled
by the particle when t = 3 s.
6. A particle travels along a straight line with an acceleration of a = (10 - 0.2s) m/s², where s is
measured in meters. Determine the velocity of the particle when s = 10 m if v = 5 m/s at s = 0.
7. Two particles A and B start from rest at the origin s = 0 and move along a straight line such
that a
(6t - 3) ft/s² and aß = (12t² - 8) ft/s², where t is in seconds. Determine the distance
between them when t = 4 s and the total distance each has travelled in t = 4 s.
=
8. When a particle is projected vertically upwards with an initial velocity of vo, it experiences an
acceleration a = - (g + kv²), where g is the acceleration due to gravity, k is a constant and v is
the velocity of the particle. Determine the maximum height reached by the particle.
Transcribed Image Text:1. A particle moves along a straight line such that its acceleration is a = (4t² - 2)m/s², where t is in seconds. When t = 0, the particle is located 2m to the left of the origin, and t = 2 s, it is 20m to the left of the origin. Determine the position of the particle when t = 4 s. 3tz ft/s², 2. A particle is moving along a straight line with the acceleration a = 12t where t is in seconds. Determine the velocity and the position of the particle as a function of time. When t = 0, v = 0 and s = 15 ft. 3. A ball is released from the bottom of an elevator which is travelling upward with a velocity of 6 m/s. The ball strikes the bottom of the elevator shaft in elevator shaft in 3s. Determine the height of the elevator from the bottom of the shaft to the instant the ball is released, and find the velocity of the ball when it strike the bottom of the shaft. 4. A particle moving along a straight line is subjected to a deceleration a = -2v m/s², where v is in m/s. If it has a velocity v = 8 m/s s = 10 m when t = 0, determine its velocity. 5. The position of the particle is given by s = (2t2 8t + 6) m, where t is in seconds. Determine the time when the velocity of the particle is zero, and the total distance travelled by the particle when t = 3 s. 6. A particle travels along a straight line with an acceleration of a = (10 - 0.2s) m/s², where s is measured in meters. Determine the velocity of the particle when s = 10 m if v = 5 m/s at s = 0. 7. Two particles A and B start from rest at the origin s = 0 and move along a straight line such that a (6t - 3) ft/s² and aß = (12t² - 8) ft/s², where t is in seconds. Determine the distance between them when t = 4 s and the total distance each has travelled in t = 4 s. = 8. When a particle is projected vertically upwards with an initial velocity of vo, it experiences an acceleration a = - (g + kv²), where g is the acceleration due to gravity, k is a constant and v is the velocity of the particle. Determine the maximum height reached by the particle.
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